University status celebrated at Lingnan

This article described how students and staff welcomed Lingnan College\u27s impending change in status after the bill conferring university status on the college was gazetted.https://commons.ln.edu.hk/lingnan_milestone_newspapers/1000/thumbnail.jp

Hugh Miller: stonemason, geologist, writer

Hugh Miller was born in 1802 in Cromarty, Ross-shire. He started his working life as a stonemason’s apprentice; he later became a social commentator and crusader. His was a household name in his lifetime, not only in Scotland but across the English-speaking world. A recent revival in Scottish history and culture, and a reassessment of the 19th century debates in science, geology and religion, have all led to a fuller appreciation of the rich and complex stories in which Hugh Miller played a part, and of the man himself. With the benefit of recent research for the 2002 conferences, this biography does full justice to the self-educated man, a figure of renown in the 19th century whose literary genius and scientific acumen still resonate in the 21s

The Maximal Entropy Measure of Fatou Boundaries

We look at the maximal entropy (MME) measure of the boundaries of connected components of the Fatou set of a rational map of degree greater than or equal to 2. We show that if there are infinitely many Fatou components, and if either the Julia set is disconnected or the map is hyperbolic, then there can be at most one Fatou component whose boundary has positive MME measure. We also replace hyperbolicity by the more general hypothesis of geometric finiteness

Curvature and Uniformization

We approach the problem of uniformization of general Riemann surfaces through consideration of the curvature equation, and in particular the problem of constructing Poincar\'e metrics (i.e., complete metrics of constant negative curvature) by solving the equation $\Delta u - e^{2u} = K_0(z)$ on general open surfaces. A few other topics are discussed, including boundary behavior of the conformal factor $e^{2u}$ giving the Poincar\'e metric when the Riemann surface has smoothly bounded compact closure, and also a curvature equation proof of Koebe's disk theorem.Comment: 26 page

Epidemic threshold and control in a dynamic network

In this paper we present a model describing susceptible-infected-susceptible-type epidemics spreading on a dynamic contact network with random link activation and deletion where link activation can be locally constrained. We use and adapt an improved effective degree compartmental modeling framework recently proposed by Lindquist et al. [ J. Math Biol. 62 143 (2010)] and Marceau et al. [ Phys. Rev. E 82 036116 (2010)]. The resulting set of ordinary differential equations (ODEs) is solved numerically, and results are compared to those obtained using individual-based stochastic network simulation. We show that the ODEs display excellent agreement with simulation for the evolution of both the disease and the network and are able to accurately capture the epidemic threshold for a wide range of parameters. We also present an analytical R0 calculation for the dynamic network model and show that, depending on the relative time scales of the network evolution and disease transmission, two limiting cases are recovered: (i) the static network case when network evolution is slow and (ii) homogeneous random mixing when the network evolution is rapid. We also use our threshold calculation to highlight the dangers of relying on local stability analysis when predicting epidemic outbreaks on evolving networks

Exact solutions for the populations of the n-level ion

We present a matrix solution to the full equations of statistical equilibrium that give the energy level populations of collisionally-excited ions in photoionised gaseous nebulae. The rationale for such a calculation is to maintain a parity between improvements in the quantum-mechanically evaluated values for collision strengths and transition probabilities from the Iron and Opacity Projects on the one hand, and 3D photoionisation codes such as MOCASSIN and astrophysical software for producing nebular diagnostics such as the Nebular package for IRAF, on the other. We have taken advantage of the fact that mathematics programs such as MATLAB and Mathematica have proven to be very adept at symbolic manipulation providing a route to exact solutions for the n-level ion. In particular, we have avoided the substitution of estimated values. We provide the matrix solution for the 5-level ion as an example and show how the equations faithfully reduce to the exact solution for the 3-level ion. Through the forbidden line ratio R23, we compare the exact solution with a) that obtained from the observed emission of the spherical planetary nebula Abell 39, b) 3D Monte-Carlo photoionisation modelling of the same nebula, c) the approximate 5-level program TEMDEN and d) the exact 3-level ion. The general solution presented here means that programs for the calculation of level populations can obtain solutions for ions with a user-specified number of excited levels. The use of a separate and updatable database of atomic and ionic constants such as that provided by NIST, means that software of more general application can now be made available; particularly for the study of high excitation objects such as active galactic nebulae (AGNs) and supernovae (SNs) where higher excited levels become significant.Comment: 8 pages, 1 figure and 1 table. Submitted to MNRA